georgechanhc wrote:

In a certain office 25% of the computers are equipped with built-in modems and infra-red ports. What percentage of the computers are not equipped with either of these devices?

1. Half of the computers that are equipped with built-in modems do not have infra-red ports

2. 35% of all computers are equipped with infra-red ports but do not have built-in modems

From S_1 we know that 25% of all computers have built-in modems but do not have infra-red ports. However, without knowing the percentage of the computers with infra-red ports but without built-in modems, we cannot answer the question. S_2 gives the opposite information. We cannot answer the question without knowing the percentage of the computers with built-in modems but without infra-red ports. From S_1 and S_2 combined it follows that 25% + 25% + 35% = 85% of all computers are equipped with at least one of the devices. Therefore, 15% are equipped with neither of them.

The correct answer is C.

My question is: How did the explanation deduce that S_1 = 25%? S_1 only says HALF of the computer with built-in modems. But we don't even know how many computers have built-in modem.

I had to do it twice as I lost the connection for some reason and I lost my response write up. That okie.

1. computers with built-in modems and infra-red ports = B&I

2. computers with only built-in modems = B

3. total computers with built-in modems (TB) = B + B&I

4. computers with only infra-red ports = I

5. total computers with infra-red ports (TI) = I + B&I

(Note: Make sure to understand the difference between "2 & 3", and "4 and 5". they are very confusing and look similar but they are not)

6. computers with neither = N

7. total computers (T) = B&I + B + I + N

T = (TB + TI - B&I) + N = (B + B&I) + (I + B&I) - B&I + N = B + I + B&I + N

St 1: "Half of the computers that are equipped with built-in modems do not have infra-red ports" means these are the computers with only B. using the above notations,

1/2 (TB) = B

TB = 2B

B + B&I = 2B

B = B&I (since B = 25%, B&I should also be 25%).

Hopy you get it. If any doubt, try with drawing ven diagram, which is very useful especially in set problems.

St 2: I = 35%.

Togather:

T = B&I + B + I + N = 25% +

100% = 25% + 25% + 35% + N

N = 15%

_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html

Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT